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STANDARD 10 - ESTIMATION
Standard 10 - Estimation - Grades 7-8
Estimation, as described in the K-12 Overview includes three primary themes: determining the reasonableness of answers, using a variety of estimation strategies in a variety of situations, and estimating the results of computations.
In seventh and eighth grade, estimation and number sense are much more important skills than algorithmic paper-and-pencil computation with whole numbers. Students should become masters at applying estimation strategies so that an answer displayed on a calculator is instinctively compared to a reasonable range in which the correct answer lies. It is critical that students understand the displays that occur on the screen and the effects of calculator rounding either because of the calculator's own operational system or because of user-defined constraints. Issues of the number of significant figures and what kinds of answers make sense in a given problem setting create new reasons to focus on reasonableness of answers.
The new estimation skills begun in fifth and sixth grade are still being developed in the seventh and eighth grades. These include skills in estimating the results of fraction and decimal computations. As students deepen their understanding of these numbers and perform operations with them, estimation ought always to be present. Estimation of quantities in fraction or decimal terms as a result of operations on those numbers is just as important for the mathematically literate adult as the same skills with whole numbers.
In addition, the seventh and eighth grades present students with opportunities to develop strategies for estimation with ratios, proportions, and percents. Estimation and number sense must play an important role in the lessons dealing with these concepts so that students feel comfortable with the relative effects of operations on them. Another new opportunity here is estimation of roots. It should be well within every eighth grader's ability, for example, to estimate the square root of 40.
Students should understand that sometimes, an estimate will be accurate enough to serve as an answer. At other times, an exact computation will need to be done, either mentally, with paper-and-pencil, or with a calculator. Even in cases where exact answers are to be calculated, however, students must understand that it is almost always a good idea to have an estimate in mind so that the computed answer can be checked against it.
Standard 10 - Estimation - Grades 7-8
Indicators and Activities
The cumulative progress indicators for grade 8 appear below in boldface type. Each indicator is followed by activities which illustrate how it can be addressed in the classroom in grades 7 and 8.
Building upon knowledge and skills gained in the preceding grades, experiences in grades 7-8 will be such that all students:
5*. Recognize when estimation is appropriate, and understand the usefulness of an estimate as distinct from an exact answer.
6. Determine the reasonableness of an answer by estimating the result of operations.
To assess students' performance, the teacher asks them to write about how they can answer this question without doing any exact computations.
If 6% sales tax is charged, can you tell whether $50 is enough by estimating? Explain. Calculate the exact price including tax.
8. Develop, apply, and explain a variety of different estimation strategies in problem situations involving quantities and measurement.
9. Use equivalent representations of numbers such as fractions, decimals, and percents to facilitate estimation.
10. Determine whether a given estimate is an overestimate or an underestimate.
Krantz, Les. America by the Numbers. New York: Houghton Mifflin, 1993. (Note: Some of the entries in this book are unsuitable for seventh- and eighth-graders.)
Green Globs and Graphing Equations. Sunburst Communications.
Hot Dog Stand. Sunburst Communications.
Survival Math. Sunburst Communications.
The Framework will be available at this site during Spring 1997. In time, we hope to post additional resources relating to this standard, such as grade-specific activities submitted teachers, and to provide a forum to discuss the Mathematics Standards.
* Activities are included here for Indicators 5 and 6, which are also listed for grade 4, since the Standards specify that students demonstrate continued progress in these indicators.